34) 13/(x-12) + 12/(x-13) = 2;

1. Combine fractions: (13(x-13) + 12(x-12))/((x-12)(x-13)) = 2.

2. Simplify numerator and denominator: (13x - 169 + 12x - 144) = 2(x^2 - 25x + 156).

3. Solve quadratic: 25x - 313 = 2x^2 - 50x + 312 -> 2x^2 - 75x + 625 = 0.

4. Use quadratic formula: x = (75 ± sqrt(75^2 - 4*2*625))/(2*2) = (75 ± sqrt(5625 - 5000))/4 = (75 ± sqrt(625))/4 = (75 ± 25)/4.

5. Solutions: x = 100/4 = 25, x = 50/4 = 12.5.